How do the principal axes of inertia depend on the symmetry of an object? Describe the...

How do the principal axes of inertia depend on the symmetry of an object? Describe the principal axes of inertia for a bowling pin that has rotational symmetry about one axis.

Solutions

Expert Solution

When an object is rotating about a fixed axis due to the symmetry of the object about that axis sometimes we can’t differentiate between snapshots of the object at different rotation angles i.e. the mass distribution of object doesn’t change. Generally, these axes pass through center of mass(COM) and are called principle axes. For example, consider a cylinder which has the axis passing through the COM and parallel to axis of cylinder as the principle axis. The moment of inertia tensor is a diagonal matrix for these principle axes.

For a bowling pin axis passing through COM and parallel to the length of pin is the principle axis of inertia and has rotational symmetry.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

On which of the following does the moment of inertia of an object depend?

On which of the following does the moment of inertia of an object depend? Check all that apply. linear speed linear acceleration angular speed angular acceleration total mass shape and density of the object location of the axis of rotation

String is wrapped around an object of mass M = 0.3 kg and moment of inertia...

String is wrapped around an object of mass M = 0.3 kg and moment of inertia I = 0.01 kgÂ·m2. You pull the string with your hand straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (see the figure). This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y0 = 0.26 m...

What is azimuthal symmetry? When to use azimuthal symmetry and and how to know whether the...

What is azimuthal symmetry? When to use azimuthal symmetry and and how to know whether the problem has azimuthal symmetry or not?

1.To see why the amount of light produced by a black object must only depend on...

1.To see why the amount of light produced by a black object must only depend on it’s temperature consider the following situation. Suppose you have two black square plates, each at the same temperature, that are placed face to face with a small gap between them. They are both perfectly black and so absorb all electromagnetic radiation incident upon them but suppose one of the plates is emitting twice the radiation of the other. Explain why this would violate the...

When a constant force acts on an object, what does the object's change in momentum depend...

When a constant force acts on an object, what does the object's change in momentum depend upon?

8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed...

8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed axis with angular speed of 10 rad/s. A constant torque of 50 Nm is applied in a direction that slows down the rotation, for 2 seconds. (i) Calculate the angular speed of the object at t = 5 s. (ii) Calculate the kinetic energy of the object at t = 5 s. 9.A disc of moment of inertia 10 kg m^2 about its center...

What does impulse do to an object? How does a large impulse affect an object differently...

What does impulse do to an object? How does a large impulse affect an object differently Than a small one? Use what you said above to answer: What does the presence of an airbag do to a person's head during an automobile collision? Answer in terms of impulse, impact, force, and time using complete sentences. So finally in terms of impulse and momentum, why do airbags make automobiles safer?

An object with a height of −0.040 m points below the principal axis (it is inverted)...

An object with a height of −0.040 m points below the principal axis (it is inverted) and is 0.140 m in front of a diverging lens. The focal length of the lens is −0.34 m. (Include the sign of the value in your answers.) (a) What is the magnification? (b) What is the image height? m. (c) What is the image distance? m.

What is radial symmetry? Which animal taxa are radially symmetric? How might radial symmetry be advantageous...

What is radial symmetry? Which animal taxa are radially symmetric? How might radial symmetry be advantageous to these types of organisms? What is bilateral symmetry, who has it, and what advantages does it convey to those animals? How do sponges fit in to all this?

Are most animals vertebrates or invertebrates? How does bilateral symmetry differ from radial symmetry? What is...

Are most animals vertebrates or invertebrates? How does bilateral symmetry differ from radial symmetry? What is cephalization?

Subjects